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### Why is there Net Work Done on a Pressure/Volume Cycle?

The area enclosed by the rectangle is said to be the Net Work Done. My question is why would there be any net workdone if it returns to its initial position (W). Shouldn't it act like a force-...
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### How can internal energy be expressed as a function of any two of $p, v, T$?

In the book of Irey, Theormodynamics, the author states that (while talking about single phase substances) For a simple compressible media, we may choose our measurable independent variables any ...
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### Isn't the equation of state for ideal gas valid in the free expansion?

I am deeply confused.... For a thermally insulated ideal gas expanding freely, I think that $PV^{\gamma}=cnst$ must hold. Through the equation $PV=nRT$, it must be that $TV^{{\gamma}-1}=\rm constant$. ...
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### Does the total energy in a volume (gas) increase linearly with increases in pressure?

If a volume has a certain pressure, then double that pressure at another time, is the total energy stored doubled? I'm sure this has to do with thermodynamics and if I remember correctly there is a ...
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### Change of specific internal energy due to temperature and volume

The change of internal energy due to temperature and volume may be written as $$dU=C_V dT + \left( T\left(\frac{\partial S}{\partial V}\right)_T-P\right) dV$$ where \left(\frac{\partial S}{\partial ...
### $p$-$V$ diagram and internal energy
I recently learned that if the initial state is equal to the final state in the $p$-$V$ diagram then the internal energy is equal to zero so that means $Q=W$. My question is how can you know that only ...